Take-home_Ex01

Published

February 4, 2024

1. Objective

We will be applying appropriate spatial point patterns analysis methods learned in class to discover the geographical and spatio-temporal distribution of Grab hailing services locations in Singapore.

2. Getting Started

2.1 Loading R packages

The R packages that we will be using in this exercise are as follows:

  • arrow: For reading parquet files (Grab-Posisi Dataset)

  • lubridate: To handle the date formatting

  • sf: Import, manage and process vector-based geospatial data in R.

  • tidyverse: a collection of packages for data science tasks

  • spatstat: Wide range of useful functions for point pattern analysis and derive kernel density estimation (KDE) layer.

  • spNetwork: provides functions to perform Spatial Point Patterns Analysis such as kernel density estimation (KDE) and K-function on network. It also can be used to build spatial matrices (‘listw’ objects like in ‘spdep’ package) to conduct any kind of traditional spatial analysis with spatial weights based on reticular distances.

  • tmap: Provides functions for plotting cartographic quality static point patterns maps or interactive maps by using leaflet API.

  • raster: reads, writes, manipulates, analyses and model of gridded spatial data (i.e. raster). In this hands-on exercise, it will be used to convert image output generate by spatstat into raster format.

  • maptools: Provides a set of tools for manipulating geographic data. In this take-home exercise, we mainly use it to convert Spatial objects into ppp format of spatstat.

  • # classInt, viridis, rgdal

Show code
pacman::p_load(arrow, lubridate, sf, tidyverse, spNetwork, tmap, 
               spatstat, raster, maptools)

2.2 Importing the datasets

The datasets that we will be using are as follow:

Using read_parquet() function from arrow package to import the grab data, then changing pingtimestamp column to datetime object

Show code
grab_df <- read_parquet("data/aspatial/part-00000.snappy.parquet")

grab_df$pingtimestamp <- as_datetime(grab_df$pingtimestamp)

Transforming the coordinate system at the same time when we are importing the data

Show code
sg_roads <- st_read(dsn = "data/geospatial", layer = "gis_osm_roads_free_1") %>% st_transform(crs = 3414)
Reading layer `gis_osm_roads_free_1' from data source 
  `/Users/jacksontan/Documents/Sashimii0219/IS415-GAA/Take-home_Ex/Take-home_Ex01/data/geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 1759836 features and 10 fields
Geometry type: LINESTRING
Dimension:     XY
Bounding box:  xmin: 99.66041 ymin: 0.8021131 xmax: 119.2601 ymax: 7.514393
Geodetic CRS:  WGS 84

Transforming the coordinate system at the same time when we are importing the data

Show code
mpsz2019 <- st_read("data/geospatial", layer = "MPSZ-2019") %>% st_transform(crs = 3414)
Reading layer `MPSZ-2019' from data source 
  `/Users/jacksontan/Documents/Sashimii0219/IS415-GAA/Take-home_Ex/Take-home_Ex01/data/geospatial' 
  using driver `ESRI Shapefile'
Simple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension:     XY
Bounding box:  xmin: 103.6057 ymin: 1.158699 xmax: 104.0885 ymax: 1.470775
Geodetic CRS:  WGS 84

3. Geospatial Data Wrangling

Before we begin exploring the data, we will first need to perform some data pre-processing on the datasets that we have imported.

3.1 Data Pre-processing - MPSZ2019

3.1.1 Excluding Outer Islands

As grab won’t be able to reach offshore places, we will exclude the outer islands from this dataset. We will do this through the following steps:

We will first take a look at the unique planning areas in Singapore using unique() on the PLN_AREA_N column of mpsz2019 dataset.

Show code
unique(mpsz2019$PLN_AREA_N)
 [1] "MARINA EAST"             "RIVER VALLEY"           
 [3] "SINGAPORE RIVER"         "WESTERN ISLANDS"        
 [5] "MUSEUM"                  "MARINE PARADE"          
 [7] "SOUTHERN ISLANDS"        "BUKIT MERAH"            
 [9] "DOWNTOWN CORE"           "STRAITS VIEW"           
[11] "QUEENSTOWN"              "OUTRAM"                 
[13] "MARINA SOUTH"            "ROCHOR"                 
[15] "KALLANG"                 "TANGLIN"                
[17] "NEWTON"                  "CLEMENTI"               
[19] "BEDOK"                   "PIONEER"                
[21] "JURONG EAST"             "ORCHARD"                
[23] "GEYLANG"                 "BOON LAY"               
[25] "BUKIT TIMAH"             "NOVENA"                 
[27] "TOA PAYOH"               "TUAS"                   
[29] "JURONG WEST"             "SERANGOON"              
[31] "BISHAN"                  "TAMPINES"               
[33] "BUKIT BATOK"             "HOUGANG"                
[35] "CHANGI BAY"              "PAYA LEBAR"             
[37] "ANG MO KIO"              "PASIR RIS"              
[39] "BUKIT PANJANG"           "TENGAH"                 
[41] "SELETAR"                 "SUNGEI KADUT"           
[43] "YISHUN"                  "MANDAI"                 
[45] "PUNGGOL"                 "CHOA CHU KANG"          
[47] "SENGKANG"                "CHANGI"                 
[49] "CENTRAL WATER CATCHMENT" "SEMBAWANG"              
[51] "WESTERN WATER CATCHMENT" "WOODLANDS"              
[53] "NORTH-EASTERN ISLANDS"   "SIMPANG"                
[55] "LIM CHU KANG"           
Show code
plot(mpsz2019)

Note that there are 3 areas with island in their name, mainly “NORTH-EASTERN ISLANDS”, “SOUTHERN ISLANDS”, and “WESTERN ISLANDS”.

To exclude the islands, we simply have to pass a condition to exclude these islands in the subset function.

Show code
mpsz2019_new <- subset(mpsz2019, !(PLN_AREA_N %in% 
            c("NORTH-EASTERN ISLANDS", "SOUTHERN ISLANDS", "WESTERN ISLANDS")))

Great! Now let’s check if we indeed removed the maps!

Show code
tmap_mode('plot')
before <- tm_shape(mpsz2019) +
  tm_polygons("PLN_AREA_N") +
  tmap_options(max.categories = 53)
after <- tm_shape(mpsz2019_new) +
  tm_polygons("PLN_AREA_N") +
  tmap_options(max.categories = 53)

tmap_arrange(before, after)

3.1.2 Invalid Geometries

We will be using the st_is_valid() function to test for invalid geometries.

Show code
test <- st_is_valid(mpsz2019_new,reason=TRUE)

# Number of invalid geometries
length(which(test!= "Valid Geometry"))
[1] 3
Show code
# Reason
test[which(test!= "Valid Geometry")]
[1] "Ring Self-intersection[26922.5243000389 27027.610899987]" 
[2] "Ring Self-intersection[38991.2589000446 31986.5599999869]"
[3] "Ring Self-intersection[14484.6860000313 31330.1319999856]"

We can see that there are 3 invalid geometries. Let’s fix them using st_make_valid().

Show code
mpsz2019_new<- st_make_valid(mpsz2019_new)
length(which(st_is_valid(mpsz2019_new) == FALSE))
[1] 0

3.1.3 Missing Values

Show code
mpsz2019_new[rowSums(is.na(mpsz2019_new))!=0,]
Simple feature collection with 0 features and 6 fields
Bounding box:  xmin: NA ymin: NA xmax: NA ymax: NA
Projected CRS: SVY21 / Singapore TM
[1] SUBZONE_N  SUBZONE_C  PLN_AREA_N PLN_AREA_C REGION_N   REGION_C   geometry  
<0 rows> (or 0-length row.names)

Using the code above, we can see that there are no missing values.

3.1.4 Creating boundary?

Show code
sg_boundary <- mpsz2019_new %>% st_union()
plot(sg_boundary)

3.2 Data Pre-processing - OpenStreetMap Road Dataset

3.2.1 Limiting the dataset

As the dataset contains data from Malaysia and Brunei as well, we will use st_intersection() to limit the data to only Singapore.

Show code
points_within_sg <- st_intersection(sg_roads, mpsz2019_new)

Now, we can see that in points_within_sg it only contain Singapore road data, combined with the other values from mpsz2019 like “PLN_AREA_N” used above.

Show code
colnames(points_within_sg)
 [1] "osm_id"     "code"       "fclass"     "name"       "ref"       
 [6] "oneway"     "maxspeed"   "layer"      "bridge"     "tunnel"    
[11] "SUBZONE_N"  "SUBZONE_C"  "PLN_AREA_N" "PLN_AREA_C" "REGION_N"  
[16] "REGION_C"   "geometry"  
Show code
head(points_within_sg)
Simple feature collection with 6 features and 16 fields
Geometry type: LINESTRING
Dimension:     XY
Bounding box:  xmin: 31466.72 ymin: 30680.54 xmax: 32815.21 ymax: 30873.74
Projected CRS: SVY21 / Singapore TM
        osm_id code        fclass               name  ref oneway maxspeed layer
4052  23946437 5122   residential          Rhu Cross <NA>      F       50     0
9668  32605139 5131 motorway_link               <NA> <NA>      F       40     0
20076 46337834 5131 motorway_link               <NA> <NA>      F       50    -2
21690 49961799 5111      motorway East Coast Parkway  ECP      F       70     1
26543 74722808 5111      motorway East Coast Parkway  ECP      F       70     1
29808 99007260 5131 motorway_link               <NA> <NA>      F       50     1
      bridge tunnel   SUBZONE_N SUBZONE_C  PLN_AREA_N PLN_AREA_C       REGION_N
4052       F      F MARINA EAST    MESZ01 MARINA EAST         ME CENTRAL REGION
9668       F      F MARINA EAST    MESZ01 MARINA EAST         ME CENTRAL REGION
20076      F      T MARINA EAST    MESZ01 MARINA EAST         ME CENTRAL REGION
21690      F      F MARINA EAST    MESZ01 MARINA EAST         ME CENTRAL REGION
26543      T      F MARINA EAST    MESZ01 MARINA EAST         ME CENTRAL REGION
29808      T      F MARINA EAST    MESZ01 MARINA EAST         ME CENTRAL REGION
      REGION_C                       geometry
4052        CR LINESTRING (31889.45 30760....
9668        CR LINESTRING (32768.57 30857....
20076       CR LINESTRING (32815.21 30873....
21690       CR LINESTRING (32365.45 30845....
26543       CR LINESTRING (31611.63 30720....
29808       CR LINESTRING (31611.63 30720....

3.2.2 Invalid Geometries

Again, using the st_is_valid() function to test for invalid geometries.

Show code
test <- st_is_valid(points_within_sg,reason=TRUE)

# Number of invalid geometries
length(which(test!= "Valid Geometry"))
[1] 0
Show code
# Reason
test[which(test!= "Valid Geometry")]
character(0)

No invalid geometries!

3.2.3 Missing Values / Dropping Columns

Show code
points_within_sg[rowSums(is.na(points_within_sg))!=0,]
Simple feature collection with 232766 features and 16 fields
Geometry type: GEOMETRY
Dimension:     XY
Bounding box:  xmin: 2679.373 ymin: 23099.51 xmax: 50957.8 ymax: 50220.06
Projected CRS: SVY21 / Singapore TM
First 10 features:
         osm_id code        fclass           name  ref oneway maxspeed layer
4052   23946437 5122   residential      Rhu Cross <NA>      F       50     0
9668   32605139 5131 motorway_link           <NA> <NA>      F       40     0
20076  46337834 5131 motorway_link           <NA> <NA>      F       50    -2
29808  99007260 5131 motorway_link           <NA> <NA>      F       50     1
45723 140562813 5131 motorway_link           <NA> <NA>      F       70    -1
45728 140562819 5131 motorway_link           <NA> <NA>      F       50     0
45731 140562823 5131 motorway_link           <NA> <NA>      F       60    -2
45733 140562826 5131 motorway_link           <NA> <NA>      F       40     0
52966 150819034 5141       service Bay East Drive <NA>      B        0     0
84664 174717984 5153       footway           <NA> <NA>      B        0     0
      bridge tunnel   SUBZONE_N SUBZONE_C  PLN_AREA_N PLN_AREA_C       REGION_N
4052       F      F MARINA EAST    MESZ01 MARINA EAST         ME CENTRAL REGION
9668       F      F MARINA EAST    MESZ01 MARINA EAST         ME CENTRAL REGION
20076      F      T MARINA EAST    MESZ01 MARINA EAST         ME CENTRAL REGION
29808      T      F MARINA EAST    MESZ01 MARINA EAST         ME CENTRAL REGION
45723      F      F MARINA EAST    MESZ01 MARINA EAST         ME CENTRAL REGION
45728      F      F MARINA EAST    MESZ01 MARINA EAST         ME CENTRAL REGION
45731      F      T MARINA EAST    MESZ01 MARINA EAST         ME CENTRAL REGION
45733      F      F MARINA EAST    MESZ01 MARINA EAST         ME CENTRAL REGION
52966      F      F MARINA EAST    MESZ01 MARINA EAST         ME CENTRAL REGION
84664      F      F MARINA EAST    MESZ01 MARINA EAST         ME CENTRAL REGION
      REGION_C                       geometry
4052        CR LINESTRING (31889.45 30760....
9668        CR LINESTRING (32768.57 30857....
20076       CR LINESTRING (32815.21 30873....
29808       CR LINESTRING (31611.63 30720....
45723       CR LINESTRING (32782.42 30754....
45728       CR LINESTRING (32645.37 30683....
45731       CR LINESTRING (32809.68 30108....
45733       CR LINESTRING (32609.11 30700....
52966       CR LINESTRING (32173.46 30036....
84664       CR LINESTRING (31750.06 30644....

By using the code above, we can see that majority of the missing values are in the ‘name’ and ‘ref’ column. Therefore, let’s drop the irrelevant columns first before we try it again!

Show code
sg_roads_new <- points_within_sg[c("osm_id", "code", "fclass", "PLN_AREA_N", "geometry")]

We only kept “osm_id”, “code”, “fclass”, and “PLN_AREA_N” columns.

Show code
sg_roads_new[rowSums(is.na(sg_roads_new))!=0,]
Simple feature collection with 0 features and 4 fields
Bounding box:  xmin: NA ymin: NA xmax: NA ymax: NA
Projected CRS: SVY21 / Singapore TM
[1] osm_id     code       fclass     PLN_AREA_N geometry  
<0 rows> (or 0-length row.names)

No more missing values here.

Our map so far:

Show code
tm_shape(sg_boundary) +
  tm_polygons() +
  tm_shape(sg_roads_new) +
  tm_lines("PLN_AREA_N")

3.3 Data Pre-processing - Grab-Posisi Dataset

The Grab-Posisi Dataset is an Aspatial dataset, different from the two we prepared above. As such, the pre-processing is slightly different too.

3.3.1 Getting the Origin and Destination Locations

The code below is a chain of dplyr pipes to group the trips by their id and extract the first pingtimestamp row of each trip in order to get the origin of it.

Show code
origin_df <- grab_df %>%
  group_by(trj_id) %>%
  arrange(pingtimestamp) %>% 
  filter(row_number()==1) %>% 
  mutate(weekday = wday(pingtimestamp,
                        label=TRUE,
                        abbr=TRUE),
         start_hr = factor(hour(pingtimestamp)),
         day = factor(mday(pingtimestamp)))
Show code
destination_df <- grab_df %>%
  group_by(trj_id) %>%
  arrange(desc(pingtimestamp)) %>% 
  # Same as previous code but desc, so ending location
  filter(row_number()==1) %>%
  mutate(weekday = wday(pingtimestamp,
                        label=TRUE,
                        abbr=TRUE),
         end_hr = factor(hour(pingtimestamp)),
         day = factor(mday(pingtimestamp)))

3.3.2 Converting to SF format from Dataframe

We will need the files in SF format first before we can use it for further geospatial analysis.

Show code
origin_sf <- st_as_sf(origin_df, 
                       coords = c("rawlng", "rawlat"),
                       crs=4326) %>%
  st_transform(crs = 3414)

dest_sf <- st_as_sf(destination_df, 
                       coords = c("rawlng", "rawlat"),
                       crs=4326) %>%
  st_transform(crs = 3414)

3.3.3 Invalid Geometries

Show code
test <- st_is_valid(origin_sf,reason=TRUE)
length(which(test!= "Valid Geometry"))
[1] 0
Show code
test <- st_is_valid(dest_sf,reason=TRUE)
length(which(test!= "Valid Geometry"))
[1] 0

3.3.4 Missing Files

Show code
origin_sf[rowSums(is.na(origin_sf))!=0,]
Simple feature collection with 0 features and 10 fields
Bounding box:  xmin: NA ymin: NA xmax: NA ymax: NA
Projected CRS: SVY21 / Singapore TM
# A tibble: 0 × 11
# Groups:   trj_id [0]
# ℹ 11 variables: trj_id <chr>, driving_mode <chr>, osname <chr>,
#   pingtimestamp <dttm>, speed <dbl>, bearing <int>, accuracy <dbl>,
#   weekday <ord>, start_hr <fct>, day <fct>, geometry <GEOMETRY [m]>
Show code
dest_sf[rowSums(is.na(dest_sf))!=0,]
Simple feature collection with 0 features and 10 fields
Bounding box:  xmin: NA ymin: NA xmax: NA ymax: NA
Projected CRS: SVY21 / Singapore TM
# A tibble: 0 × 11
# Groups:   trj_id [0]
# ℹ 11 variables: trj_id <chr>, driving_mode <chr>, osname <chr>,
#   pingtimestamp <dttm>, speed <dbl>, bearing <int>, accuracy <dbl>,
#   weekday <ord>, end_hr <fct>, day <fct>, geometry <GEOMETRY [m]>

No missing values, we are almost ready.

3.3.5 Removing points on the islands

Show code
origin_sf_new <- st_intersection(origin_sf, mpsz2019_new)
dest_sf_new <- st_intersection(dest_sf, mpsz2019_new)

To verify that the points that we removed is indeed from the islands, here’s a chunk of code to prove:

Show code
# Finding out points removed
diff_id <- origin_sf$trj_id[!(origin_sf$trj_id %in% origin_sf_new$trj_id)]

# Extracting full information of these points
outliers <- origin_sf[(origin_sf$trj_id %in% diff_id), ]

# Checking where these places are from
unique(st_intersection(outliers, mpsz2019)$PLN_AREA_N)
[1] "WESTERN ISLANDS"  "SOUTHERN ISLANDS"

They are indeed from “WESTERN ISLANDS” and “SOUTHERN ISLANDS”.

3.3.6 Dropping Unnecessary Columns

Now that our grab dataset is almost ready, we need to decide which column we should drop. Here are the columns in both origin_sf_new and dest_sf_new:

Show code
colnames(origin_sf_new)
 [1] "trj_id"        "driving_mode"  "osname"        "pingtimestamp"
 [5] "speed"         "bearing"       "accuracy"      "weekday"      
 [9] "start_hr"      "day"           "SUBZONE_N"     "SUBZONE_C"    
[13] "PLN_AREA_N"    "PLN_AREA_C"    "REGION_N"      "REGION_C"     
[17] "geometry"     
Show code
colnames(dest_sf_new)
 [1] "trj_id"        "driving_mode"  "osname"        "pingtimestamp"
 [5] "speed"         "bearing"       "accuracy"      "weekday"      
 [9] "end_hr"        "day"           "SUBZONE_N"     "SUBZONE_C"    
[13] "PLN_AREA_N"    "PLN_AREA_C"    "REGION_N"      "REGION_C"     
[17] "geometry"     

We will definitely be dropping the columns merged from mpsz2019_new (other than PLN_AREA_N), but what about “driving_mode”, “osname”, “speed”, “bearing”, and “accuracy”? Let’s first take a look at them.

Show code
unique(origin_sf_new$driving_mode)
[1] "car"

Seeing that there is only 1 constant in the column, it is safe for us to drop this column.

Show code
unique(origin_sf_new$osname)
[1] "ios"     "android"

There are 2 values, mainly “ios” and “android”. Arguments can be made that we can analyse the behavior of both type in terms of using grab hailing services, but that’s not what we will doing so we will drop this as well.

As we are analysing start/stop points, speed will not be a relevant factor hence we will be dropping them.

Not relevant as well, hence dropping.

According to research paper published on Grab website, this is the definition of the accuracy column:

“…the accuracy level roughly indicates the radius of the circle within which the true location lies with a certain probability. The lower the accuracy level, the more precise the reported GPS ping is.”

With that, let’s take a look at the distribution of accuracy score.

Show code
plot(origin_sf_new$accuracy)

Show code
ggplot(origin_sf_new, 
       aes(x=rownames(origin_sf_new), y=accuracy)) + 
  geom_point(size = 2)

Show code
ggplot(dest_sf_new, 
       aes(x=rownames(dest_sf_new), y=accuracy)) + 
  geom_point(size = 2)

From the plot, we can see that there are 3 clear outliers with accuracy above 180~ for origin_sf_new, and 1 for dest_sf_new. Now let’s extract these trips.

Show code
origin_sf_new[origin_sf_new$accuracy > 180, ]
Simple feature collection with 3 features and 16 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 18132.25 ymin: 30203 xmax: 28937.76 ymax: 36948.91
Projected CRS: SVY21 / Singapore TM
# A tibble: 3 × 17
  trj_id driving_mode osname pingtimestamp              speed bearing accuracy
  <chr>  <chr>        <chr>  <dttm>                     <dbl>   <int>    <dbl>
1 78815  car          ios    2019-04-21 13:20:13  0.000000101      68      200
2 67866  car          ios    2019-04-18 16:46:16 -1                13      547
3 4579   car          ios    2019-04-21 10:35:22 13.0             108      200
# ℹ 10 more variables: weekday <ord>, start_hr <fct>, day <fct>,
#   SUBZONE_N <chr>, SUBZONE_C <chr>, PLN_AREA_N <chr>, PLN_AREA_C <chr>,
#   REGION_N <chr>, REGION_C <chr>, geometry <POINT [m]>
Show code
dest_sf_new[dest_sf_new$accuracy > 500, ]
Simple feature collection with 1 feature and 16 fields
Geometry type: POINT
Dimension:     XY
Bounding box:  xmin: 33721.09 ymin: 34502.5 xmax: 33721.09 ymax: 34502.5
Projected CRS: SVY21 / Singapore TM
# A tibble: 1 × 17
  trj_id driving_mode osname pingtimestamp       speed bearing accuracy weekday
  <chr>  <chr>        <chr>  <dttm>              <dbl>   <int>    <dbl> <ord>  
1 68340  car          ios    2019-04-12 11:55:48    -1      10     1414 Fri    
# ℹ 9 more variables: end_hr <fct>, day <fct>, SUBZONE_N <chr>,
#   SUBZONE_C <chr>, PLN_AREA_N <chr>, PLN_AREA_C <chr>, REGION_N <chr>,
#   REGION_C <chr>, geometry <POINT [m]>

To ensure that our data is of utmost accuracy, we will drop these trips, before we drop the accuracy column as well (as we will not need it anymore).

Show code
origin_sf_new <- subset(origin_sf_new, accuracy < 180)
dest_sf_new <- subset(dest_sf_new, accuracy < 500)

With that done, we can now drop the columns that we don’t need.

Show code
origin_sf_new <- origin_sf_new[, c(1, 4,  8:10, 13, 17)]
dest_sf_new <- dest_sf_new[, c(1, 4,  8:10, 13, 17)]

3.3.7 Duplicated Points

Lastly, let’s check for duplicated points on the map.

Show code
# Check for any duplicates
any(duplicated(origin_sf_new))
[1] FALSE
Show code
# Count the number of duplicates
sum(multiplicity(origin_sf_new) > 1)
[1] 0

No duplicated points!

3.4 Verifying Coordinate System

It is important for the data to be in the right coordinate reference system (CRS). In this assignment, all spatial data will be projected in EPSG:3414, which is a projected coordinate system for Singapore.

Show code
st_crs(mpsz2019_new)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]
Show code
st_crs(sg_roads_new)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]
Show code
st_crs(origin_sf_new)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]
Show code
st_crs(dest_sf_new)
Coordinate Reference System:
  User input: EPSG:3414 
  wkt:
PROJCRS["SVY21 / Singapore TM",
    BASEGEOGCRS["SVY21",
        DATUM["SVY21",
            ELLIPSOID["WGS 84",6378137,298.257223563,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["degree",0.0174532925199433]],
        ID["EPSG",4757]],
    CONVERSION["Singapore Transverse Mercator",
        METHOD["Transverse Mercator",
            ID["EPSG",9807]],
        PARAMETER["Latitude of natural origin",1.36666666666667,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8801]],
        PARAMETER["Longitude of natural origin",103.833333333333,
            ANGLEUNIT["degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["Scale factor at natural origin",1,
            SCALEUNIT["unity",1],
            ID["EPSG",8805]],
        PARAMETER["False easting",28001.642,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",38744.572,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["northing (N)",north,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["easting (E)",east,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Cadastre, engineering survey, topographic mapping."],
        AREA["Singapore - onshore and offshore."],
        BBOX[1.13,103.59,1.47,104.07]],
    ID["EPSG",3414]]

They are all in the correct CRS!

3.5 Plotting Spatial Data

Finally, plotting all three datasets together to ensure that they have a consistent projection system.

Show code
tm_shape(sg_boundary) +
  tm_polygons() +
tm_shape(sg_roads_new) + 
  tm_lines("PLN_AREA_N") + 
tm_shape(origin_sf_new) +
  tm_dots()

3.6 Exploratory Data Analysis

Before we begin our Geospatial Analysis, let’s first take a closer look at the Grab dataset.

3.6.1 Day of the Week

The distribution of the trips across all 7 days of the week looks even.

Show code
ggplot(origin_sf_new, aes(x=weekday)) + geom_bar()

Show code
ggplot(dest_sf_new, aes(x=weekday)) + geom_bar()

3.6.2 Planning Area

First let us look at the top 10 planning areas for grab ride origin points. Tampines is the Planning Area with the most origin points.

Show code
origin_pl_area <- origin_sf_new %>%
  group_by(PLN_AREA_N) %>%
  summarise(total_count=n()) %>%
  top_n(10, total_count) %>%
  .$PLN_AREA_N

ggplot(origin_sf_new[origin_sf_new$PLN_AREA_N %in% origin_pl_area,], 
       aes(x=PLN_AREA_N)) + geom_bar() +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1)) +
  labs(title = "Trips Origin Distribution by Planning Area",
       x = "Planning Area",
       y = "Number of Trips")

Then for the destination points.

Show code
dest_pl_area <- dest_sf_new %>%
  group_by(PLN_AREA_N) %>%
  summarise(total_count=n()) %>%
  top_n(10, total_count) %>%
  .$PLN_AREA_N

ggplot(dest_sf_new[dest_sf_new$PLN_AREA_N %in% dest_pl_area,], 
       aes(x=PLN_AREA_N)) + geom_bar() +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust=1)) +
  labs(title = "Trips Destination Distribution by Planning Area",
       x = "Planning Area",
       y = "Number of Trips")

6 out of 10 of the Planning Areas remains the same for destination points, mainly TAMPINES, WOODLANDS, YISHUN, QUEENSTOWN, BUKIT MERAH, and CHANGI. This time however, the Planning Area with the most destination points is Changi.

3.6.3 Starting Hour

Show code
origin_sf_new$start_hr <- factor(origin_sf_new$start_hr, levels = 0:23)

ggplot(origin_sf_new, aes(x = start_hr)) +
  geom_bar() +
  labs(title = "Trips Distribution by Start Hour",
       x = "Start Hour",
       y = "Number of Trips")

From the graph, we can see that the starting hour peaks at midnight (12am - 1am) and morning (9am - 10am), the former probably due to the lack of public transport after operating hours, and the latter from rush hour.

4. Kernel Density Estimation (KDE) Layers

4.1 Converting data format

4.1.1 Creating point ppp objects

In the code chunk below, as.ppp() function is used to derive a ppp object layer directly from a sf tibble data.frame.

Show code
origin_ppp <- as.ppp(origin_sf_new)
summary(origin_ppp)
Marked planar point pattern:  27872 points
Average intensity 2.636568e-05 points per square unit

Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units

marks are of type 'character'
Summary:
   Length     Class      Mode 
    27872 character character 

Window: rectangle = [3661.47, 49845.23] x [26795.39, 49685.08] units
                    (46180 x 22890 units)
Window area = 1057130000 square units
Show code
dest_ppp <- as.ppp(dest_sf_new)
summary(dest_ppp)
Marked planar point pattern:  27820 points
Average intensity 2.642188e-05 points per square unit

Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units

marks are of type 'character'
Summary:
   Length     Class      Mode 
    27820 character character 

Window: rectangle = [3638.69, 50024.92] x [26770.54, 49469.41] units
                    (46390 x 22700 units)
Window area = 1052920000 square units

4.1.2 Creating owin objects

In the code chunk as.owin() is used to create an owin object class from polygon sf tibble data.frame. In this case, we will be converting the sg_boundary polygon.

Show code
sg_boundary_owin <- as.owin(sg_boundary)

4.1.3 Combining point events object and owin object

We will now combine singapore’s boundary and the origin and destination points into one.

Show code
originSG_ppp = origin_ppp[sg_boundary_owin]
destSG_ppp = dest_ppp[sg_boundary_owin]
Show code
plot(destSG_ppp)

Show code
summary(destSG_ppp)
Marked planar point pattern:  27820 points
Average intensity 4.185996e-05 points per square unit

Coordinates are given to 3 decimal places
i.e. rounded to the nearest multiple of 0.001 units

marks are of type 'character'
Summary:
   Length     Class      Mode 
    27820 character character 

Window: polygonal boundary
37 separate polygons (29 holes)
                  vertices         area relative.area
polygon 1            12666  6.63014e+08      9.98e-01
polygon 2              285  1.61128e+06      2.42e-03
polygon 3               27  1.50315e+04      2.26e-05
polygon 4 (hole)        41 -4.01660e+04     -6.04e-05
polygon 5 (hole)       317 -5.11280e+04     -7.69e-05
polygon 6 (hole)         3 -4.14099e-04     -6.23e-13
polygon 7               30  2.80002e+04      4.21e-05
polygon 8 (hole)         4 -2.86396e-01     -4.31e-10
polygon 9 (hole)         3 -1.81439e-04     -2.73e-13
polygon 10 (hole)        3 -8.68789e-04     -1.31e-12
polygon 11 (hole)        3 -5.99535e-04     -9.02e-13
polygon 12 (hole)        3 -3.04561e-04     -4.58e-13
polygon 13 (hole)        3 -4.46076e-04     -6.71e-13
polygon 14 (hole)        3 -3.39794e-04     -5.11e-13
polygon 15 (hole)        3 -4.52043e-05     -6.80e-14
polygon 16 (hole)        3 -3.90173e-05     -5.87e-14
polygon 17 (hole)        3 -9.59850e-05     -1.44e-13
polygon 18 (hole)        4 -2.54488e-04     -3.83e-13
polygon 19 (hole)        4 -4.28453e-01     -6.45e-10
polygon 20 (hole)        4 -2.18616e-04     -3.29e-13
polygon 21 (hole)        5 -2.44411e-04     -3.68e-13
polygon 22 (hole)        5 -3.64686e-02     -5.49e-11
polygon 23              71  8.18750e+03      1.23e-05
polygon 24 (hole)        6 -8.37554e-01     -1.26e-09
polygon 25 (hole)       38 -7.79904e+03     -1.17e-05
polygon 26 (hole)        3 -3.41897e-05     -5.14e-14
polygon 27 (hole)        3 -3.65499e-03     -5.50e-12
polygon 28 (hole)        3 -4.95057e-02     -7.45e-11
polygon 29              91  1.49663e+04      2.25e-05
polygon 30 (hole)        5 -2.92235e-04     -4.40e-13
polygon 31 (hole)        3 -7.43616e-06     -1.12e-14
polygon 32 (hole)      270 -1.21455e+03     -1.83e-06
polygon 33 (hole)       19 -4.39650e+00     -6.62e-09
polygon 34 (hole)       35 -1.38385e+02     -2.08e-07
polygon 35 (hole)       23 -1.99656e+01     -3.00e-08
polygon 36              71  5.63061e+03      8.47e-06
polygon 37              10  1.99717e+02      3.01e-07
enclosing rectangle: [2667.54, 55941.94] x [21448.47, 50256.33] units
                     (53270 x 28810 units)
Window area = 664597000 square units
Fraction of frame area: 0.433

4.1.4 Rescale

The density values of the output range from 0 to 0.000035 which is way too small to comprehend, and it is computed in “number of points per square meter”. Therefore, we are going to use rescale() to covert the unit of measurement from meter to kilometer.

Show code
originSG_ppp.km <- rescale(originSG_ppp, 1000, "km")
destSG_ppp.km <- rescale(destSG_ppp, 1000, "km")

4.2 Deriving Traditional Kernel Density Estimation (KDE) Layers

4.2.1 Automatic bandwidth selection method

We will first compute the kernel density by using density() of the spatstat package, with the default method bw.diggle().

Show code
kde_originSG_bw <- density(originSG_ppp.km,
                              sigma=bw.ppl,
                              edge=TRUE,
                            kernel="gaussian") 

plot(kde_originSG_bw, main = "Kernel Density Estimation Layer")

Looking at all the different methods, we can see that bw.diggle() is still the best among the automatic bandwidth selection method.

Show code
bw.CvL(originSG_ppp.km)
   sigma 
1.542325 
Show code
bw.scott(originSG_ppp.km)
  sigma.x   sigma.y 
1.5924296 0.9284281 
Show code
bw.ppl(originSG_ppp.km)
     sigma 
0.08744077 
Show code
bw.diggle(originSG_ppp.km)
     sigma 
0.01078274 
Show code
kde_originSG_ppl <- density(originSG_ppp.km, 
                               sigma=bw.ppl, 
                               edge=TRUE,
                               kernel="gaussian")
par(mfrow=c(1,2))
plot(kde_originSG_bw, main = "bw.diggle")
plot(kde_originSG_ppl, main = "bw.ppl")

4.2.2 Computing KDE by using fixed bandwidth

Having tried automatic bandwidth selection method, let’s try computing KDE by using a fixed bandwidth defined by us. In our case, we will define a fixed bandwidth of 800m (or 0.8km).

Show code
kde_originSG_500 <- density(originSG_ppp.km, sigma=0.5, edge=TRUE, kernel="gaussian")
plot(kde_originSG_500)

4.2.3 Computing KDE by using adaptive bandwidth

Fixed bandwidth method, however, is very sensitive to highly skewed distribution of spatial point patterns over geographical units, for example urban versus rural. To overcome this, we can try using adaptive bandwidth instead.

Show code
kde_childcareSG_adaptive <- adaptive.density(originSG_ppp.km, method="kernel")
plot(kde_childcareSG_adaptive)

4.2.4 Method we are using

As the KDE layer using fixed bandwidth with gaussian kernel plots a graph that allows for meaningful analysis at a glance, we will be using that for the steps moving forward.

Show code
kde_originSG_500 <- density(originSG_ppp.km, sigma=0.5, edge=TRUE, kernel="gaussian")
plot(kde_originSG_500)

Show code
kde_destSG_500 <- density(destSG_ppp.km, sigma=0.5, edge=TRUE, kernel="gaussian")
plot(kde_destSG_500)

Show code
par(mfrow=c(1,2))
plot(kde_originSG_500, main = "Origin KDE Layer")
plot(kde_destSG_500, main = "Destination KDE layer")

4.3 Combining KDE layers

4.3.1 Converting KDE layers into grid object

In order for us to map the KDE layer of these points to our map, we first need to convert it into grid object.

Show code
gridded_kde_originSG_500 <- as.SpatialGridDataFrame.im(kde_originSG_500)
spplot(gridded_kde_originSG_500)

Show code
gridded_kde_destSG_500 <- as.SpatialGridDataFrame.im(kde_destSG_500)
spplot(gridded_kde_destSG_500)

4.3.2 Converting KDE layers into grid object

We will then convert the gridded kernel density objects into RasterLayer object by using raster() of raster package. As the RasterLayer object does not include CRS information, we will need to manually assign it to them as well.

Show code
kde_originSG_500_raster <- raster(gridded_kde_originSG_500)
projection(kde_originSG_500_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_originSG_500_raster
class      : RasterLayer 
dimensions : 128, 128, 16384  (nrow, ncol, ncell)
resolution : 0.4162063, 0.2250614  (x, y)
extent     : 2.667538, 55.94194, 21.44847, 50.25633  (xmin, xmax, ymin, ymax)
crs        : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +datum=WGS84 +units=km +no_defs 
source     : memory
names      : v 
values     : -1.923671e-14, 596.2208  (min, max)
Show code
kde_destSG_500_raster <- raster(gridded_kde_destSG_500)
projection(kde_destSG_500_raster) <- CRS("+init=EPSG:3414 +datum=WGS84 +units=km")
kde_destSG_500_raster
class      : RasterLayer 
dimensions : 128, 128, 16384  (nrow, ncol, ncell)
resolution : 0.4162063, 0.2250614  (x, y)
extent     : 2.667538, 55.94194, 21.44847, 50.25633  (xmin, xmax, ymin, ymax)
crs        : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +datum=WGS84 +units=km +no_defs 
source     : memory
names      : v 
values     : -7.516604e-15, 520.156  (min, max)

4.3.3 Overlaying KDE layer on tmap plot

To further explore the map, we will now be overlaying the KDE layer both onto OpenStreetMap of Singapore, and also on the Singapore Planning Area layer and OSM road layer that we have pre-processed.

4.3.3.1 Overlay on OpenStreetMap

Show code
tmap_mode("view")
tm_basemap(leaflet::providers$OpenStreetMap) +
tm_shape(kde_originSG_500_raster) + 
  tm_raster("v", alpha = 0.7,
          palette = "YlOrRd") +
  tm_layout(legend.position = c("right", "bottom"), frame = FALSE)
Show code
tmap_mode("plot")
Show code
tmap_mode("view")
tm_basemap(leaflet::providers$OpenStreetMap) +
tm_shape(kde_destSG_500_raster) + 
  tm_raster("v", alpha = 0.7,
          palette = "YlOrRd") +
  tm_layout(legend.position = c("right", "bottom"), frame = FALSE)
Show code
tmap_mode("plot")

As you can see from the plot, there are certain planning areas that are hotspots for hailing of Grab ride service, in particular Central Region (Orchard, Newton etc), Woodlands, Punggol, Tampines, and most notably Changi (where the airport lies).

4.3.3.2 Overlay on Planning Area and OSM Road Layers

To further confirm our observation, let’s plot the KDE layer over our Planning Area and OSM Road Layers.

Show code
tmap_mode("view")
tm_shape(mpsz2019_new) +
  tm_polygons("PLN_AREA_N") +
tm_shape(kde_originSG_500_raster) + 
  tm_raster("v", alpha = 0.7,
          palette = "YlOrRd")
Show code
tmap_mode("view")
tm_shape(mpsz2019_new) +
  tm_polygons("PLN_AREA_N") +
tm_shape(kde_destSG_500_raster) + 
  tm_raster("v", alpha = 0.7,
          palette = "YlOrRd")

The common overlapping Planning Areas include “TAMPINES”, “CHANGI”, “WOODLANDS”, and “NOVENA”, so let’s do a further analysis on these areas.

4.4 In-depth KDE Computation

4.4.1 Data Preparation

To do in-depth KDE computation on these 4 planning areas, we will first need to extract their respective boundaries. In the code below, we extracted their boundaries and converted them to sp’s Spatial* class.

Show code
mpsz <- as_Spatial(mpsz2019_new)
cg = mpsz[mpsz@data$PLN_AREA_N == "CHANGI",]
tp = mpsz[mpsz@data$PLN_AREA_N == "TAMPINES",]
wl = mpsz[mpsz@data$PLN_AREA_N == "WOODLANDS",]
nv = mpsz[mpsz@data$PLN_AREA_N == "NOVENA",]

Plotting down these boundaries.

Show code
par(mfrow=c(2,2))
plot(cg, main = "CHANGI")
plot(tp, main = "TAMPINES")
plot(wl, main = "WOODLANDS")
plot(nv, main = "NOVENA")

Turning the spatial point data frame into generic sp format, then into owin object as done previously.

Show code
cg_sp = as(cg, "SpatialPolygons")
tp_sp = as(tp, "SpatialPolygons")
wl_sp = as(wl, "SpatialPolygons")
nv_sp = as(nv, "SpatialPolygons")

cg_owin = as(cg_sp, "owin")
tp_owin = as(tp_sp, "owin")
wl_owin = as(wl_sp, "owin")
nv_owin = as(nv_sp, "owin")

By using the code below, we will be able to extract grab origin and destination points for these specific areas.

Show code
origin_cg_ppp = origin_ppp[cg_owin]
origin_tp_ppp = origin_ppp[tp_owin]
origin_wl_ppp = origin_ppp[wl_owin]
origin_nv_ppp = origin_ppp[nv_owin]

dest_cg_ppp = dest_ppp[cg_owin]
dest_tp_ppp = dest_ppp[tp_owin]
dest_wl_ppp = dest_ppp[wl_owin]
dest_nv_ppp = dest_ppp[nv_owin]

Next up is the rescale() function used previously as well.

Show code
origin_cg_ppp.km = rescale(origin_cg_ppp, 1000, "km")
origin_tp_ppp.km = rescale(origin_tp_ppp, 1000, "km")
origin_wl_ppp.km = rescale(origin_wl_ppp, 1000, "km")
origin_nv_ppp.km = rescale(origin_nv_ppp, 1000, "km")

dest_cg_ppp.km = rescale(dest_cg_ppp, 1000, "km")
dest_tp_ppp.km = rescale(dest_tp_ppp, 1000, "km")
dest_wl_ppp.km = rescale(dest_wl_ppp, 1000, "km")
dest_nv_ppp.km = rescale(dest_nv_ppp, 1000, "km")

Finally, we plot the four planning areas and the grab hailing origin and destination points

Show code
par(mfrow=c(2,4))
plot(origin_cg_ppp.km, main = "CHANGI ORIGIN")
plot(origin_tp_ppp.km, main = "TAMPINES ORIGIN")
plot(origin_wl_ppp.km, main = "WOODLANDS ORIGIN")
plot(origin_nv_ppp.km, main = "NOVENA ORIGIN")

plot(dest_cg_ppp.km, main = "CHANGI DESTINATION")
plot(dest_tp_ppp.km, main = "TAMPINES DESTINATION")
plot(dest_wl_ppp.km, main = "WOODLANDS DESTINATION")
plot(dest_nv_ppp.km, main = "NOVENA DESTINATION")

4.4.2 Computing KDE

We will now be computing the KDE of each planning area using the fixed bandwidth method.

Show code
par(mfrow=c(1,2))

plot(density(origin_cg_ppp.km, 
             sigma=0.5, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Changi Origin")

plot(density(dest_cg_ppp.km, 
             sigma=0.5, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Changi Destination")

Show code
tmap_mode('plot')
tm_shape(mpsz2019_new[mpsz2019_new$PLN_AREA_N == "CHANGI", ]) + 
  tm_polygons('SUBZONE_N')

The hotspot in Changi area is centered around Changi Airport, indicating a likely surge in use of Grab services due to the constant flow of passengers arriving and departing from Singapore.

Show code
par(mfrow=c(1,2))

plot(density(origin_tp_ppp.km, 
             sigma=0.5, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Tampines Origin")

plot(density(dest_tp_ppp.km, 
             sigma=0.5, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Tampines Destination")

Show code
tmap_mode('plot')
tm_shape(mpsz2019_new[mpsz2019_new$PLN_AREA_N == "TAMPINES", ]) + 
  tm_polygons('SUBZONE_N')

The hotspot in Tampines area is mainly concentrated around the stretch from Tampines West to Tampines East, encompassing the bulk of where most residents of Tampines currently live (Tampines West, Tampines, Tampines East).

Show code
par(mfrow=c(1,2))

plot(density(origin_wl_ppp.km, 
             sigma=0.5, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Woodlands Origin")

plot(density(dest_wl_ppp.km, 
             sigma=0.5, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Woodlands Destination")

Show code
tmap_mode('plot')
tm_shape(mpsz2019_new[mpsz2019_new$PLN_AREA_N == "WOODLANDS", ]) + 
  tm_polygons('SUBZONE_N')

The rides are concentrated around the lower half of Woodlands area, ranging from Woodlands West to Woodlands South, then Woodlands East. However, one prominent hotspot shared across both the origin and destination map is the Woodlands West region, indicating that this might either be the area with the wealthiest residents in Woodlands, or that there are just more residents concentrated here.

Show code
par(mfrow=c(1,2))

plot(density(origin_nv_ppp.km, 
             sigma=0.5, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Novena Origin")

plot(density(dest_nv_ppp.km, 
             sigma=0.5, 
             edge=TRUE, 
             kernel="gaussian"),
     main="Novena Destination")

Show code
tmap_mode('plot')
tm_shape(mpsz2019_new[mpsz2019_new$PLN_AREA_N == "NOVENA", ]) + 
  tm_polygons('SUBZONE_N')

The Novena area’s notable hotspots present an interesting distinction. Origin points predominantly converge around the affluent Moulmein area, revealing a concentration in the wealthier section of town. Conversely, the destination points gravitate towards the Malcolm area, characterized by a cluster of prestigious schools, as illustrated in the figure below.

Moulmein Area

Google Map View of Malcolm Area, characterized by Prestigious Schools

4.5 Nearest Neighbour Analysis

In this section, we will perform the Clark-Evans test of aggregation for a spatial point pattern by using clarkevans.test() of statspat package, to test whether the distribution of Grab ride hailing origin points are randomly distributed.

Using 95% confidence interval, the test hypotheses are:

Ho = The distribution of Grab ride hailing origin points are randomly distributed.

H1= The distribution of Grab ride hailing origin points are not randomly distributed.

For this section, we will be making use of the ppp object.

Clark-Evans Test

Show code
clarkevans.test(originSG_ppp,
                correction="none",
                clipregion="sg_owin",
                alternative=c("clustered"),
                nsim=99)

    Clark-Evans test
    No edge correction
    Z-test

data:  originSG_ppp
R = 0.28008, p-value < 2.2e-16
alternative hypothesis: clustered (R < 1)
Show code
clarkevans.test(origin_cg_ppp,
                correction="none",
                clipregion="sg_owin",
                alternative=c("clustered"),
                nsim=99)

    Clark-Evans test
    No edge correction
    Z-test

data:  origin_cg_ppp
R = 0.11647, p-value < 2.2e-16
alternative hypothesis: clustered (R < 1)
Show code
clarkevans.test(origin_tp_ppp,
                correction="none",
                clipregion="sg_owin",
                alternative=c("clustered"),
                nsim=99)

    Clark-Evans test
    No edge correction
    Z-test

data:  origin_tp_ppp
R = 0.31668, p-value < 2.2e-16
alternative hypothesis: clustered (R < 1)
Show code
clarkevans.test(origin_wl_ppp,
                correction="none",
                clipregion="sg_owin",
                alternative=c("clustered"),
                nsim=99)

    Clark-Evans test
    No edge correction
    Z-test

data:  origin_wl_ppp
R = 0.31908, p-value < 2.2e-16
alternative hypothesis: clustered (R < 1)
Show code
clarkevans.test(origin_nv_ppp,
                correction="none",
                clipregion="sg_owin",
                alternative=c("clustered"),
                nsim=99)

    Clark-Evans test
    No edge correction
    Z-test

data:  origin_nv_ppp
R = 0.35838, p-value < 2.2e-16
alternative hypothesis: clustered (R < 1)

Having performed the Clark-Evans Test on all 4 planning area and Singapore as a whole, all of their p-values are <2.2e-16 < 0.05, thus we reject Ho. This means that the distribution of Grab ride hailing origin points are not randomly distributed which we explored in earlier sections.

Furthermore, as their R value ranges from 0.11647 to 0.35838 which is <1, this suggests that the points are clustering.

5. Network Kernel Density Estimation (NKDE) Layers

In this section, we will be using appropriate functions of spNetwork package:

  • to derive network constrained kernel density estimation (NetKDE), and
  • to perform network G-function and k-function analysis,

where in this case the network refers to OSM’s Road Map of Singapore.

However, due to limitations in computational power, we will be limiting the area of scope down to the 4 areas identified in the previous section, Changi, Tampines, Woodlands, and Novena, and only the Origin points.

5.1 Data Preparation

5.1.1 Initial Data Pre-processing

Before we begin, let us first convert our sg_roads_new data from SFC_GEOMETRY to SFC_LINESTRING.

Show code
sg_roads_linestring <- st_cast(sg_roads_new, "LINESTRING")

5.1.2 Narrowing down the scope

Then, let us narrow down the scope of our data to the 4 areas mentioned.

Show code
# Roads
cg_roads <- sg_roads_linestring %>% filter(PLN_AREA_N == "CHANGI")
tp_roads <- sg_roads_linestring %>% filter(PLN_AREA_N == "TAMPINES")
wl_roads <- sg_roads_linestring %>% filter(PLN_AREA_N == "WOODLANDS")
nv_roads <- sg_roads_linestring %>% filter(PLN_AREA_N == "NOVENA")

# Grab Origin Points
cg_origin <- origin_sf_new %>% filter(PLN_AREA_N == "CHANGI")
tp_origin <- origin_sf_new %>% filter(PLN_AREA_N == "TAMPINES")
wl_origin <- origin_sf_new %>% filter(PLN_AREA_N == "WOODLANDS")
nv_origin <- origin_sf_new %>% filter(PLN_AREA_N == "NOVENA")

5.1.3 Visualising the data

Before we begin our analysis, let us visualise our geospatial data to make sure everything falls into place.

Show code
tm_shape(cg_roads) +
  tm_lines("PLN_AREA_N") +
tm_shape(cg_origin) +
  tm_dots()

Show code
tm_shape(tp_roads) +
  tm_lines("PLN_AREA_N") +
tm_shape(tp_origin) +
  tm_dots()

Show code
tm_shape(wl_roads) +
  tm_lines("PLN_AREA_N") +
tm_shape(wl_origin) +
  tm_dots()

Show code
tm_shape(nv_roads) +
  tm_lines("PLN_AREA_N") +
tm_shape(nv_origin) +
  tm_dots()

5.2 Network Constrained KDE (NetKDE) Analysis

We will now perform NetKDE analysis by using appropriate functions provided in spNetwork package.

5.2.1 Preparing the lixels objects

Before we can compute NetKDE, the SpatialLines object need to be cut into lixels with a specified minimal distance, and this can be done using lixelize_lines() of spNetwork package.

Show code
cg_lixels <- lixelize_lines(cg_roads, 
                         700, 
                         mindist = 350)

tp_lixels <- lixelize_lines(tp_roads, 
                         700, 
                         mindist = 350)

wl_lixels <- lixelize_lines(wl_roads, 
                         700, 
                         mindist = 350)

nv_lixels <- lixelize_lines(nv_roads, 
                         700, 
                         mindist = 350)

5.2.2 Generating line centre points

Next, we will use lines_center() of spNetwork to generate a SpatialPointsDataFrame (i.e. samples) with line centre points.

Show code
cg_lines_center <- lines_center(cg_lixels)
tp_lines_center <- lines_center(tp_lixels)
wl_lines_center <- lines_center(wl_lixels)
nv_lines_center <- lines_center(nv_lixels)

5.2.3 Computing NetKDE

We are now ready to compute NetKDE. As the code is fairly long, we will split it into 4 tabs.

Show code
# Origin
cg_o_densities <- nkde(cg_roads, 
                  events = cg_origin,
                  w = rep(1,nrow(cg_origin)),
                  samples = cg_lines_center,
                  kernel_name = "quartic", # kernel method
                  bw = 300, 
                  div= "bw", 
                  method = "simple", 
                  # method used to calculate NKDE. spNetwork supports 3 popular                                     methods, namely simple, discontinuous, and continuous
                  digits = 1, 
                  tol = 1,
                  grid_shape = c(1,1), 
                  max_depth = 8,
                  agg = 5, 
                  # we aggregate events within a 5m radius (faster calculation)
                  sparse = TRUE,
                  verbose = FALSE)
Show code
tp_o_densities <- nkde(tp_roads, 
                  events = tp_origin,
                  w = rep(1,nrow(tp_origin)),
                  samples = tp_lines_center,
                  kernel_name = "quartic", # kernel method
                  bw = 300, 
                  div= "bw", 
                  method = "simple", 
                  # method used to calculate NKDE. spNetwork supports 3 popular                                     methods, namely simple, discontinuous, and continuous
                  digits = 1, 
                  tol = 1,
                  grid_shape = c(1,1), 
                  max_depth = 8,
                  agg = 5, 
                  # we aggregate events within a 5m radius (faster calculation)
                  sparse = TRUE,
                  verbose = FALSE)
Show code
wl_o_densities <- nkde(wl_roads, 
                  events = wl_origin,
                  w = rep(1,nrow(wl_origin)),
                  samples = wl_lines_center,
                  kernel_name = "quartic", # kernel method
                  bw = 300, 
                  div= "bw", 
                  method = "simple", 
                  # method used to calculate NKDE. spNetwork supports 3 popular                                     methods, namely simple, discontinuous, and continuous
                  digits = 1, 
                  tol = 1,
                  grid_shape = c(1,1), 
                  max_depth = 8,
                  agg = 5, 
                  # we aggregate events within a 5m radius (faster calculation)
                  sparse = TRUE,
                  verbose = FALSE)
Show code
nv_o_densities <- nkde(nv_roads, 
                  events = nv_origin,
                  w = rep(1,nrow(nv_origin)),
                  samples = nv_lines_center,
                  kernel_name = "quartic", # kernel method
                  bw = 300, 
                  div= "bw", 
                  method = "simple", 
                  # method used to calculate NKDE. spNetwork supports 3 popular                                     methods, namely simple, discontinuous, and continuous
                  digits = 1, 
                  tol = 1,
                  grid_shape = c(1,1), 
                  max_depth = 8,
                  agg = 5, 
                  # we aggregate events within a 5m radius (faster calculation)
                  sparse = TRUE,
                  verbose = FALSE)

5.2.4 Reinsert Density

Before we are able to visualise, we first need to insert the computed values back into lines_center and lixels objects as density field.

Show code
cg_lines_center$o_density <- cg_o_densities
cg_lixels$o_density <- cg_o_densities

tp_lines_center$o_density <- tp_o_densities
tp_lixels$o_density <- tp_o_densities

wl_lines_center$o_density <- wl_o_densities
wl_lixels$o_density <- wl_o_densities

nv_lines_center$o_density <- nv_o_densities
nv_lixels$o_density <- nv_o_densities

Since svy21 projection system is in meter, the computed density values are very small i.e. 0.0000005. We will thus need to rescale the density values from number of events per meter to number of events per kilometer.

Show code
cg_lines_center$o_density <- cg_lines_center$o_density*1000
cg_lixels$o_density <- cg_lixels$o_density*1000

tp_lines_center$o_density <- tp_lines_center$o_density*1000
tp_lixels$o_density <- tp_lixels$o_density*1000

wl_lines_center$o_density <- wl_lines_center$o_density*1000
wl_lixels$o_density <- wl_lixels$o_density*1000

nv_lines_center$o_density <- nv_lines_center$o_density*1000
nv_lixels$o_density <- nv_lixels$o_density*1000

5.2.5 Visualising NetKDE

Show code
tmap_mode('view')
tm_basemap(leaflet::providers$OpenStreetMap) +
tm_shape(cg_lixels)+
  tm_lines(col="o_density")+
tm_shape(cg_origin)+
  tm_dots(alpha=0.2)
Show code
tmap_mode('plot')

This tmap plot further reinforces our observation above that the grab ride traffic are from incoming tourists or locals returning home form the airport, as you can see the denser area being the Changi Airport Terminals. However, it is worth highlighting that there some slight traffic along the Changi Village area and infront of the Japanese School as well.

Show code
tmap_mode('view')
tm_basemap(leaflet::providers$OpenStreetMap) +
tm_shape(tp_lixels)+
  tm_lines(col="o_density")+
tm_shape(tp_origin)+
  tm_dots(alpha=0.2)
Show code
tmap_mode('plot')

As we have discovered earlier, a huge portion of the grab rides indeed originated from Tampines East, one of the more populated area of Tampines. Particularly along Tampines Avenue 2, there seems to be a higher density, presumably due to it being more convenient to get a ride along the main road.

Surprisingly, the other higher density area in this network density map is the area around Changi General Hospital.

Show code
tmap_mode('view')
tm_basemap(leaflet::providers$OpenStreetMap) +
tm_shape(wl_lixels)+
  tm_lines(col="o_density")+
tm_shape(wl_origin)+
  tm_dots(alpha=0.2)
Show code
tmap_mode('plot')

There are 3 main points of to focus on with higher density, mainly:

  • Along the route to Woodlands Checkpoint, showing that a significant portion of the rides in Woodlands are people coming in from Malaysia.

  • Around the main hub of Woodlands, along the Woodlands MRT stretch. No surprises here, as the area is perhaps the most dense in terms of human traffic due to concentration of malls, bus interchange, and MRT station.

  • 3 different points around the Sembawang Air Base, which I assume is the entrance. This make sense as well, as military bases in Singapore are generally more inaccessible.

Show code
tmap_mode('view')
tm_basemap(leaflet::providers$OpenStreetMap) +
tm_shape(nv_lixels)+
  tm_lines(col="o_density")+
tm_shape(nv_origin)+
  tm_dots(alpha=0.2)
Show code
tmap_mode('plot')

Network KDE indicates that the majority of the traffic is along Moulmein Road, which is the main road next to several of the moderately wealthier estates in Singapore.

5.3 Network Constrained G- and K-Function Analysis

We are now going to perform complete spatial randomness (CSR) test by using kfunctions() of spNetwork package. The null hypothesis is defined as:

  • The observed spatial point events (i.e distribution of Grab ride hailing points) are uniformly distributed over a street network in the 4 Planning Area specified above.

The CSR test is based on the assumption of the binomial point process which implies the hypothesis that the childcare centres are randomly and independently distributed over the street network.

If this hypothesis is rejected, we may infer that the distribution of Grab ride hailing points are spatially interacting and dependent on each other; as a result, they may form nonrandom patterns.

Show code
kfun_cg <- kfunctions(cg_roads, 
                             cg_origin[c("trj_id","PLN_AREA_N", "geometry")],
                             start = 0,
                             # A double, the start value for evaluating the k and                                  g functions.
                             end = 1000, 
                             #  A double, the last value for evaluating the k                                 and g functions.
                             step = 50, 
                             # A double, the jump between two evaluations of the                               k and g function
                             width = 50,
                             # The width of each donut for the g-function
                             nsim = 50,
                             # number of Monte Carlo simulations required.
                             resolution = 50,
                             verbose = FALSE,
                             agg = 5,
                             conf_int = 0.05
                             #  A double indicating the width confidence interval                               (default = 0.05).
                             )

kfun_cg
$plotk


$plotg


$values
       obs_k    lower_k    upper_k    obs_g    lower_g    upper_g distances
1    0.00000   0.000000   0.000000 14.86145  0.4461755  0.7511913         0
2   36.75689   2.019968   2.496221 43.40340  2.2709191  2.8562247        50
3   79.23030   4.583725   5.556897 41.90507  2.8016060  3.6727370       100
4  121.95096   7.672079   9.409359 42.98638  3.2656802  4.0585737       150
5  166.35078  11.235579  13.685485 47.23408  3.7421175  4.7955567       200
6  214.49640  15.308914  18.505767 49.64395  4.2015786  5.3166485       250
7  264.37654  19.992466  24.131122 49.89859  4.7239620  5.9886796       300
8  316.81416  24.932872  30.210956 52.19405  5.2199586  6.6048004       350
9  369.73892  30.563578  36.891779 54.99879  5.3710826  7.1639038       400
10 423.85570  36.494687  44.055130 52.66643  5.9796380  7.4672589       450
11 477.36355  42.508831  52.146997 55.36046  6.1335298  8.2415155       500
12 531.87151  48.793484  60.498673 54.89546  6.5003607  8.4005740       550
13 587.96637  55.568230  69.424029 55.21653  7.0631545  8.9803438       600
14 643.18290  63.166315  78.573395 55.12058  7.6466148  9.3647043       650
15 698.60978  70.894858  88.092914 53.94332  7.9446187  9.8370821       700
16 749.05825  79.270153  98.843567 53.11297  8.3716039 10.7417962       750
17 802.93515  87.815023 109.878016 49.17157  8.5435789 11.3819049       800
18 852.30969  96.533899 121.149946 50.21966  8.9650285 11.6786172       850
19 900.47377 105.675700 133.278983 47.30420  9.2109970 12.2740715       900
20 946.48263 115.147981 146.065473 45.53648  9.6949997 12.6516046       950
21 991.41387 124.980819 158.995891 42.06376 10.1140504 12.9809774      1000

The blue line represents the empirical network K-function of the Grab ride hailing origin points in Changi planning area. The gray envelop represents the results of the 50 simulations in the interval 2.5% - 97.5%. Because the blue line is above the gray area, we can infer that these origin points in Changi planning area are in clusters, which reinforces our observations made above.

Show code
kfun_tp <- kfunctions(tp_roads, 
                             tp_origin[c("trj_id","PLN_AREA_N", "geometry")],
                             start = 0,
                             # A double, the start value for evaluating the k and                                  g functions.
                             end = 1000, 
                             #  A double, the last value for evaluating the k                                 and g functions.
                             step = 50, 
                             # A double, the jump between two evaluations of the                               k and g function
                             width = 50,
                             # The width of each donut for the g-function
                             nsim = 50,
                             # number of Monte Carlo simulations required.
                             resolution = 50,
                             verbose = FALSE,
                             agg = 10,
                             conf_int = 0.05
                             #  A double indicating the width confidence interval                               (default = 0.05).
                             )

kfun_tp
$plotk


$plotg


$values
       obs_k    lower_k    upper_k     obs_g    lower_g    upper_g distances
1    0.00000   0.000000   0.000000  3.544369  0.4931031  0.7408737         0
2   10.43806   1.620871   1.964641 14.896712  1.9071936  2.3622016        50
3   26.84334   3.873358   4.567299 17.212894  2.5247915  3.0936277       100
4   44.52556   6.756396   7.916164 17.877273  3.0530945  3.7410921       150
5   63.16474  10.317527  11.843465 19.330982  3.6918733  4.4359469       200
6   82.52925  14.456027  16.522763 18.724508  4.3565567  5.2714489       250
7  102.07051  19.215935  22.071392 20.833454  5.1580778  6.1194460       300
8  122.50168  24.821554  28.389847 20.988882  6.0018083  6.9711003       350
9  144.84065  31.594560  35.788070 22.921066  6.8362436  8.2480484       400
10 167.65810  39.226534  44.155280 22.872304  7.6878979  9.1405406       450
11 190.66450  47.813782  53.640048 23.615920  8.7041230 10.2329560       500
12 215.64575  57.096950  64.539668 25.459724  9.7016054 11.6002656       550
13 241.81557  67.730210  76.690484 26.828100 10.8112397 12.8473472       600
14 268.85090  79.241942  89.695240 27.711907 11.8027792 13.9879147       650
15 297.63862  91.640072 104.478276 29.711138 12.9002232 14.8322547       700
16 329.33375 105.425168 120.121957 31.756083 13.8733246 16.2621928       750
17 360.65707 119.826491 136.554511 32.469224 14.8148834 17.5516361       800
18 393.75715 135.278172 154.473841 35.346167 15.9898889 18.4788710       850
19 429.61227 151.940821 173.437282 35.693594 17.0946471 19.7666381       900
20 466.66205 170.017103 193.629671 39.131297 18.3231382 21.0064054       950
21 506.48820 188.550374 214.972837 39.405581 19.4365821 22.2755820      1000

Similar to Changi planning area, as the blue line is above the grey area, we can infer that the Tampines planning area consists of mainly origin points in clusters.

Show code
kfun_wl <- kfunctions(wl_roads, 
                             wl_origin[c("trj_id","PLN_AREA_N", "geometry")],
                             start = 0,
                             # A double, the start value for evaluating the k and                                  g functions.
                             end = 1000, 
                             #  A double, the last value for evaluating the k                                 and g functions.
                             step = 50, 
                             # A double, the jump between two evaluations of the                               k and g function
                             width = 50,
                             # The width of each donut for the g-function
                             nsim = 50,
                             # number of Monte Carlo simulations required.
                             resolution = 50,
                             verbose = FALSE,
                             agg = 5,
                             conf_int = 0.05
                             #  A double indicating the width confidence interval                               (default = 0.05).
                             )

kfun_wl
$plotk


$plotg


$values
        obs_k    lower_k    upper_k    obs_g    lower_g   upper_g distances
1     0.00000   0.000000   0.000000 12.80481  0.8283325  1.169309         0
2    30.08326   2.694329   3.320027 35.47919  3.4987435  4.144916        50
3    67.77057   6.696310   7.833856 39.66965  4.4945029  5.329532       100
4   108.36633  11.794698  13.716184 41.09708  5.4632827  6.603316       150
5   149.89203  18.159981  20.817571 42.13034  6.6163277  7.858348       200
6   193.36561  25.461706  29.251294 44.11650  7.8648538  9.307021       250
7   237.89542  34.440571  39.139047 45.81948  9.3141009 10.895567       300
8   285.19973  44.412707  50.532686 47.25456 10.5875020 12.704352       350
9   332.27061  55.634135  63.959365 48.52127 12.0356010 14.756527       400
10  383.29084  68.848039  79.531978 52.89924 14.0841406 16.859791       450
11  437.26544  84.058053  97.215127 54.76294 16.2578199 19.149808       500
12  492.18911 101.544117 117.474545 55.70436 18.0872695 21.447479       550
13  547.99297 120.409395 139.796854 57.94692 20.1604927 23.949315       600
14  608.33170 141.840801 165.070277 60.72525 22.6043511 27.274700       650
15  669.64247 165.786864 193.269556 62.01109 24.7049366 29.893639       700
16  732.69448 192.257341 224.227073 64.49475 26.8307797 32.114007       750
17  799.31698 220.573532 256.881438 68.91482 29.6441253 33.955511       800
18  871.09049 252.149093 292.669460 73.95102 31.6385143 36.871035       850
19  945.99058 286.000704 330.509849 76.33518 34.3395404 39.320634       900
20 1024.72905 321.252960 370.565822 81.14559 35.9127791 42.329534       950
21 1109.01653 358.614030 413.918286 86.31191 38.8296424 44.251977      1000

Similar to Changi planning area, as the blue line is above the grey area, we can infer that the Woodlands planning area consists of mainly origin points in clusters.

Show code
kfun_nv <- kfunctions(nv_roads, 
                             nv_origin[c("trj_id","PLN_AREA_N", "geometry")],
                             start = 0,
                             # A double, the start value for evaluating the k and                                  g functions.
                             end = 1000, 
                             #  A double, the last value for evaluating the k                                 and g functions.
                             step = 50, 
                             # A double, the jump between two evaluations of the                               k and g function
                             width = 50,
                             # The width of each donut for the g-function
                             nsim = 50,
                             # number of Monte Carlo simulations required.
                             resolution = 50,
                             verbose = FALSE,
                             agg = 5,
                             conf_int = 0.05
                             #  A double indicating the width confidence interval                               (default = 0.05).
                             )

kfun_nv
$plotk


$plotg


$values
        obs_k    lower_k    upper_k     obs_g    lower_g   upper_g distances
1    0.000000  0.0000000  0.0000000  2.070894 0.08958496 0.2059969         0
2    4.899254  0.3517849  0.5415156  5.799959 0.45642204 0.6624189        50
3   10.932279  0.8788552  1.1545293  5.931059 0.57514033 0.7903627       100
4   16.831777  1.5742919  2.0667664  5.841231 0.73051804 1.0077702       150
5   22.590463  2.4164876  3.1404507  6.110714 0.94416240 1.3201036       200
6   28.919677  3.5219758  4.5742957  6.732225 1.14918815 1.6539230       250
7   36.047630  4.8746117  6.3067572  7.460558 1.36392501 2.0769631       300
8   43.869927  6.4028972  8.4839875  8.091780 1.54406605 2.3122146       350
9   52.602640  8.1564804 10.8985329  8.999769 1.87752120 2.6040334       400
10  61.765070 10.2221543 13.7583326  9.453763 2.10949527 2.9575177       450
11  70.978483 12.4049684 16.8102908  9.152719 2.24229466 3.2418104       500
12  80.264729 14.8764452 20.2679305  9.232835 2.54127538 3.5231897       550
13  89.281492 17.7072329 23.8202536  9.490180 2.81464304 3.9288712       600
14  99.725788 20.6885429 27.6858812 10.415163 3.03642046 4.2420544       650
15 110.301184 23.9052257 31.8700331 11.077946 3.31318701 4.4697799       700
16 121.383985 27.3786460 36.4747974 11.230896 3.70490880 4.8441431       750
17 132.750836 31.2936789 41.5554059 11.612056 3.77033739 5.2514026       800
18 144.807176 35.4540386 46.8736938 11.956801 4.07393088 5.5997886       850
19 156.674149 39.9629057 52.4884132 12.357384 4.27883524 5.6366908       900
20 169.582638 44.3949337 58.3363206 13.102711 4.45484906 5.9826490       950
21 182.794599 48.7655389 64.4963187 13.190111 4.52865347 6.3786194      1000

Similar to Changi planning area, as the blue line is above the grey area, we can infer that the Novena planning area consists of mainly origin points in clusters.

The results of our G- and K-Function Analysis on all four planning area shows a spatial pattern of clustering among the grab origin points, which supports the idea that grab rides are commonly booked at the same location within an area, possibly due to designated pickup points or taxi stands.

6. Conclusion

In conclusion, our analysis of Grab ride-hailing origin points in the specific planning areas of Changi, Tampines, Woodlands, and Novena, and also the whole of Singapore uncovered noteworthy spatial patterns. The observed clustering of origin points within these areas suggests a localized preference for specific pickup locations, potentially driven by factors such as designated pickup points, popular landmarks, transportation hubs, or simply area with higher population density.

These findings hold practical implications for both Grab and urban planners as the identified clusters can guide Grab in optimizing their service by strategically placing vehicles or promoting the use of specific pickup points, ultimately enhancing the efficiency and user experience. Urban planners, on the other hand, can leverage this information to make informed decisions regarding infrastructure development, such as improving the accessibility of popular pickup locations or adjusting traffic flow in areas with high ride-hailing activity.

Moreover, understanding the spatial dynamics of Grab ride-hailing services contributes to a broader perspective on urban mobility patterns. This knowledge can be valuable for city officials, transportation authorities, and policymakers in crafting policies that support sustainable and efficient transportation solutions. By aligning urban planning efforts with the observed ride-hailing patterns, cities can work towards creating more resilient, user-friendly, and accessible transportation systems.

In essence, our analysis not only sheds light on the localized behaviors of Grab users but also opens avenues for strategic decision-making that can enhance the overall urban mobility landscape. As technology continues to shape the future of transportation, such spatial insights play a crucial role in fostering innovation and creating urban environments that are responsive to the evolving needs of their residents.